For the first time to our knowledge the observation of near-IR multiple higher-order stopgaps in three-dimensional photonio crystals (PhCs) fabricated using the direct-laser-writing method in thick chalcogenide glass films is reported. The fabrication and etching conditions necessary to realize well-defined structures are presented. The fabricated PhCs exhibit higher-order stopgaps, which are only evident in high-quality structures. The higher-order stopgaps observed permit these high-refractive-index and high-nonlinear PhCs to be used directly as functional photonic devices operating at telecommunication wavelengths without further miniaturizing structural dimensions.